An homotopical algebra approach to the computation of higher limits

TL;DR

This paper develops a homotopical algebra framework to compute higher limits of functors in a model category setting, providing explicit methods and vanishing bounds for these limits.

Contribution

It introduces a model category structure for functors from filtered posets to cochain complexes, enabling computation of higher limits via fibrant replacements.

Findings

Established a model category structure for functors to cochain complexes.

Provided an explicit procedure for fibrant replacement.

Derived vanishing bounds for higher limits.

Abstract

In this paper, we introduce a model category structure in the category of functors from a filtered poset to cochain complexes in which higher limits of functors that take values in $R$-modules can be computed by means of a fibrant replacement. We explicitly describe a procedure to compute the fibrant replacement and, finally, deduce some vanishing bounds for the higher limits.